First-Order Logic

Synonyms

First-order predicate calculus; First-order predicate logic; Predicate calculus; Predicate logic; Resolution

Definition

First-order predicate logic – first-order logic for short – is the logic of properties of, and relations between, objects and their parts. Like any logic, it consists of three parts: syntax governs the formation of well-formed formulae, semantics ascribes meaning to well-formed formulae and formalizes the notion of deductive consequence, and proof procedures allow the inference of deductive consequences by syntactic means. A number of variants of first-order logic exist, mainly differing in their syntax and proof systems. In machine learning, the main use of first-order logic is in learning from structured data, inductive logic programming and relational data mining.

Motivation and Background

The interest in logic arises from a desire to formalize human, mathematical and scientific reasoning, and goes back to at least the Greek philosophers. Aristotle devised...